July 3 (Reuters) - Stricter rules for abortion clinics were approved by the North Carolina Senate on Wednesday, adding that state to the ranks of a growing number nationwide seeking to tighten regulations.

The bill passed the Republican-majority state Senate on Wednesday on a vote of 29-12. Supporters maintain the bill is designed to protect the safety of women who seek an abortion, while opponents argue it could shut down all but one of the state's clinics.

The package of anti-abortion amendments was attached to an unrelated bill that would ban sharia, Islamic law in the state.

The amendments would require abortion clinics in the state to meet the same safety standards as ambulatory surgery centers, limit healthcare coverage for abortion and that a doctor be present when women take the RU-486 pill to induce abortion.

"We are very encouraged in North Carolina because for so many years, we were shut out," said Barbara Holt, president of North Carolina Right to Life, noting that anti-abortion bills were for years introduced in the state legislature under a Democratic majority, only to die in committee.

The move comes as lawmakers in Texas and Ohio have pushed hard for abortion limits in the past week, angering supporters of abortion rights. The tightened standards for abortion clinics are being considered in five states, and are already on the books in nine more, according to abortion rights advocates.

"A fuse has been lit that is burning across this country. Women have been shut down, shut out and told to shut up, but we demand to be heard," said Cecile Richards, president of Planned Parenthood Action Fund. "These attacks on women's health are dangerous and deeply unpopular, and that's why politicians are trying to sneak them in with special sessions, midnight votes, hearings without witnesses and other underhanded tactics."

The North Carolina House of Representatives has already passed the sharia bill without the last-minute abortion provisions, which were added by state senators without public notice in a late-day committee hearing and put to a preliminary vote on the Senate floor in Raleigh on Tuesday night.

The bill now goes back to the House for approval of the changes. If the bill is not approved, it may be sent to a conference committee to decide whether the abortion restrictions stay in the bill before it goes to the governor.

The hasty action was decried not only by supporters of abortion rights, but by the state's Republican governor.

Governor Pat McCrory warned lawmakers that railroading a bill through the general assembly was not the way his party should be passing legislation.

"When the Democrats were in power, this is the way they did business," McCrory said in a statement. "It was not right then and it is not right now. Regardless of what party is in charge or what important issue is being discussed, the process must be appropriate and thorough."

The North Carolina abortion restrictions are similar to those proposed in Texas, where the measure provoked strong protests and a filibuster in the state legislature that stalled - but did not defeat - the proposals.

Texas Democratic state Senator Wendy Davis galvanized abortion rights supporters nationwide with her 11-hour filibuster of the restrictions, but Republican Governor Rick Perry called the legislature back into session this week to consider the restrictions again.

A Texas House committee voted to move forward with a proposal to ban most abortions after 20 weeks of pregnancy and toughen standards for clinics, after at least 2,000 people sought to testify for and against the measure at an eight-hour hearing.

The nine states that require abortion clinics to meet the same safety standards as ambulatory surgery centers for all abortions are Alabama, Georgia, Illinois, Indiana, Kansas, Missouri, Pennsylvania, Tennessee and Virginia, according to the National Abortion Rights Action League.

Twenty-five states have passed less stringent variations of those laws, NARAL said, including some that require later-term abortions to be performed in a hospital.

The group does not keep statistics on the number of clinics that have shut down because of the regulations, just the number of those in each state that would have to make costly upgrades to conform to the new laws. (Reporting by Karen Brooks, additional reporting by Brendan O'Brien; editing by Gunna Dickson, G Crosse)